On the 2-modular reduction of the Steinberg representation of the symplectic group
classification
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grouprepresentationsteinbergsymplecticabovecharacteristicconstituentsdegree
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We show that in characteristic 2, the Steinberg representation of the symplectic group Sp(2n,q), q a power of an odd prime p, has two irreducible constituents lying just above the socle that are isomorphic to the two Weil modules of degree (q^n-1)/2.
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